John believes that the amount of sleep he gets the night before a test and his score on that test are inversely related.  On his first exam, he got eight hours of sleep and scored 70 on the exam.  To the nearest tenth, how many hours does John believe he must sleep the night before his second exam so that the average of his two exam scores is an 80?
Solution: First, to average an 80, he must score a 90 on his second exam.  Now, since score and hours of sleep are inversely related, their product is a constant.  Thus $70\cdot 8 = 90 \cdot h \Rightarrow h = 56/9 \approx \boxed{6.2}$.